In order to feed back channel state information over the air from a User Equipment to a Base Station, it needs to be quantified and the quantized CSI needs to be mapped into a sequence of bits. The feedback can be performed between any two communicating devices (e.g. feedback between two user equipments, between two base stations, etc.). The terminology “Base Station” (BS) and “User Equipment” (UE) will be used in the following merely for the sake of simplicity.
The User Equipment knows a CSI vector “h0” through some non-precise process and wants to feed back a normalized version of this vector denoted by “h” to the base station.
The size of the vector “h” (denoted by “D” in the following) can e.g. correspond to the number of antennas of the Base Station. Since the UE cannot send h with infinite precision, it has to send a “compact” representation of this vector “h”. This feedback is performed by transmitting a sequence of B bits (b1, . . . , bB) representing an approximation of “h” to the Base Station.
Current standardized codebooks are only available for low dimensions (small B) and low number of bits (small B). Some automatic designs have been proposed for large dimension. However, their performance and/or their complexity can be suboptimal.